Stereological estimation of volume ratios by systematic sections

Two related problems are explored. Firstly, a single opaque solid Ω1 of arbitrary size and shape, containing an arbitrarily shaped phase Ω2, is considered. The problem is to estimate the minimum number of systematic sections m, necessary to estimate the volume ratio v = V(Ω2)/V(Ω1) with a coefficient of error of at most γ0 with a probability 1 ‐ α. Secondly, we consider a population of such specimens. The second problem is to estimate the optimum number n of specimens to be sampled and the number m of systematic sections per specimen in order to estimate the mean volume ratio of the population with a relative error of at most ∍0 with a probability 1 ‐ α.